1. Field of the Invention
The present invention relates to the field of vibratory sensors, for example, hemispherical resonator gyroscopes ("HRG"s), and more particularly to a vibratory sensor with a self-calibrating feature and a low noise digital conversion to improve the performance of the sensor.
2. Description of Related Art
Vibratory sensors for measuring are known in the art for measuring an angular rate of a body about a predetermined axis. These sensors are of critical importance in space applications, such as the orienting of satellites and space vehicles. Sensors such as hemispherical resonator gyroscopes ("HRGs") are reliable and have a long active life, making the gyro especially suited for this purpose. The present invention, while particularly well suited for HRG applications, is readily adaptable to other types of sensors where an oscillating member conveys a signal to be interpreted at very high accuracy.
An HRG is typically comprised of a forcer electrode assembly, a hemispherical thin-walled quartz shell, and a pick-off electrode assembly joined together with a rare-earth metal such as indium. The unit is housed in a vacuum chamber with electrical feeds to communicate voltage signals from the gyro to a microprocessor for interpretation. The general operation of the gyroscope is discussed in the Letters Patent to Loper, Jr. et al., U.S. Pat. No. 4,951,508, which is fully incorporated herein by reference.
The hemispherical resonator 101 is a bell-shaped thin walled structure with a rim that can be made to deform from a circular profile to an elliptical profile when subjected to certain external electrical fields. The resonator is supported by an integral stem which itself is supported by the housing for the pick-off and forcer electrodes. By applying a cyclical forcing voltage, a standing wave pattern can be established in the resonator. To establish the standing wave, the hemispherical resonator is initially biased at a voltage of known magnitude, and then a varying electrical field is applied at the forcer electrodes. If the forcer electrodes apply the appropriate varying electrical field at angular intervals of 90 degrees, the resonator will flexure in a standing wave such as that shown in FIG. 1.
The primary harmonic resonating wave has four nodes a,b,c,d and four antinodes e,f,g,h around the perimeter of the resonator, alternating and equal spaced forty-five degrees apart. Nodes are points on the standing wave where displacement is a minimum, and antinodes are points on the standing wave where displacement is a maximum. Operation of the HRG requires precise tracking of the standing wave movement, which in turn requires that the location of the nodes and antinodes be accurately determined.
It is a physical property of the gyroscope that if an unrestrained resonator is rotated about an axis normal to the page (see FIG. 2), the standing wave will precess in an opposite direction to the original rotation due to Coriolis force. Moreover, the amount of the angular precess will be 0.3 times the angular displacement of the resonator, where 0.3 is a geometric property of the resonator's hemispherical shape and holds constant for any rotation angle and any rotation rate. For example, if the resonator of FIG. 1 is rotated ninety degrees in the counter-clockwise direction, as indicated by the angular displacement of the notch 201, the standing wave will precess twenty-seven degrees clockwise as shown in FIG. 2. In this manner when an HRG is rotated about its primary axis, by measuring the change in the angular position of the standing wave information about the rotation of the HRG can be determined.
The position of the standing wave both before and after the rotation of the gyroscope is determined by the pick-off electrodes positioned about the external annular component of the housing. By measuring the capacitance across the gap formed between the pick-off electrodes and the resonator, the distance across the gap can be accurately determined. This information is processed by a microprocessor in a manner such that the exact position of the standing wave is determined. By measuring the change in position of the standing wave, the rotation of the gyro can readily be determined.
The HRGs operate in one of two modes - whole angle mode and force rebalance mode. In whole angle mode, the standing wave is allowed to precess unhindered under the influence of the Coriolis force caused by the rotation of the gyro as just described. The instantaneous position of the standing wave is evaluated by computing the arctangent of the ratio of the amplitude of the two pickoff signals. The gyro's dynamic range is limited solely by the resolution and processing of the pickoff signal estimation.
In the force rebalance mode, the standing wave is constrained such that it does not precess under the influence of the Coriolis force, and the magnitude of the restraining force is used to calculate the rotation rate of the gyro. In this mode, an additional forcing signal is included which holds the standing wave at a fixed azimuthal location. The amount of force necessary to maintain the standing wave fixed is proportional to the input rotational rate. For force rebalance gyros, the case-oriented control and readout processing is eliminated, and the output noise performance can be optimized because the dynamic range requirements of the pick-off signal estimation are greatly reduced.
When operating in a whole angle mode, the prior art HRG typically operated as follows with reference to FIG. 3. Voltages from four pick-off electrode pairs 100 deliver an output each having a sinusoidal function. The signals are multiplied by a fixed excitation voltage, such that the signals take the form:
V.sub.1 =A cos (.omega.t) cos (.theta.) EQU V.sub.2 =-A cos (.omega.t) cos (.theta.) EQU V.sub.3 =A cos (.omega.t) sin (.theta.) EQU V.sub.4 =-A cos (.omega.t) sin (.theta.)
where A is the product of the excitation voltage across the pickoff gap and the ratio of the radial displacement of the resonator at the antinode relative to the pickoff gap, .omega. is the natural frequency of the resonator for the given conditions, and .theta. is the precession angle of the standing wave. Signals V.sub.1 and V.sub.2 are differenced to form a resultant `cosine` signal S.sub.1 and signals V.sub.3 and V.sub.4 are differenced to form a resultant `sine` signal S.sub.2. These two differential outputs of the gyro are routed to a two channel multiplexor 100 so that only one digital conversion process is required. The output of the multiplexor is summed with the output of a conventional 18 bit digital-to-analog (DAC) converter 120 which has been commanded to the estimate of the negative of the positive peak value of the signal being addressed by the multiplexor. The signal 110 is subsequently amplified (Gain) 130 and then sampled by a sixteen bit analog-to-digital converter (ADC) 140. The ADC 140 samples the combined signal once at the time of the peak of the signal. In the same manner the negative peak of the same gyro signal is processed according to the above description. The DAC 120 commands and the ADC values are combined to compute the estimate of the gyro standing wave pattern using a formula such as: EQU .theta..sub.estimate =ARCTANGENT ((Sin_DAC_command*Gain+Sin_ADC_output)/ Cos_DAC_command*Gain+Cos_ADC_output)).
The above described circuit has inherent limitations which are undesirable. For example, the performance of the above-described HRG is limited by the noise of the DAC 120, which typically only has an effective accuracy of 16 bits. Furthermore, the DAC linearity is also only 16 bits, and the effective low sample rate which generates unwanted noise (due to the alias of the higher frequency noise signals) cannot be analog filtered out of the signal prior to sampling, further contributing to the degradation of the HRG's performance. In view of the limitations of the prior art, what is needed is a low noise, moderate bandwidth resolver to digital converter with a higher bit accuracy than the previous art.